Epidemic processes with vaccination and immunity loss studied with the BLUES function method
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Epidemic processes with vaccination and immunity loss studied with the BLUES function method. / Berx, Jonas; Indekeu, Joseph O.
In: Physica A: Statistical Mechanics and its Applications, Vol. 590, 126724, 15.03.2022.Research output: Contribution to journal › Journal article › Research › peer-review
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TY - JOUR
T1 - Epidemic processes with vaccination and immunity loss studied with the BLUES function method
AU - Berx, Jonas
AU - Indekeu, Joseph O.
N1 - Publisher Copyright: © 2021
PY - 2022/3/15
Y1 - 2022/3/15
N2 - The Beyond-Linear-Use-of-Equation-Superposition (BLUES) function method is extended to coupled nonlinear ordinary differential equations and applied to the epidemiological SIRS model with vaccination. Accurate analytic approximations are obtained for the time evolution of the susceptible and infected population fractions. The results are compared with those obtained with alternative methods, notably Adomian decomposition, variational iteration and homotopy perturbation. In contrast with these methods, the BLUES iteration converges rapidly, globally, and captures the exact asymptotic behavior for long times. The time of the infection peak is calculated using the BLUES approximants and the results are compared with numerical solutions, which indicate that the method is able to generate useful analytic expressions that coincide with the (numerically) exact ones already for a small number of iterations.
AB - The Beyond-Linear-Use-of-Equation-Superposition (BLUES) function method is extended to coupled nonlinear ordinary differential equations and applied to the epidemiological SIRS model with vaccination. Accurate analytic approximations are obtained for the time evolution of the susceptible and infected population fractions. The results are compared with those obtained with alternative methods, notably Adomian decomposition, variational iteration and homotopy perturbation. In contrast with these methods, the BLUES iteration converges rapidly, globally, and captures the exact asymptotic behavior for long times. The time of the infection peak is calculated using the BLUES approximants and the results are compared with numerical solutions, which indicate that the method is able to generate useful analytic expressions that coincide with the (numerically) exact ones already for a small number of iterations.
KW - Analytic iteration
KW - Coupled ODEs
KW - Epidemic processes
KW - Matrix BLUES function method
KW - Optimal choice of linear subsystem
KW - SIRS model
U2 - 10.1016/j.physa.2021.126724
DO - 10.1016/j.physa.2021.126724
M3 - Journal article
AN - SCOPUS:85121769492
VL - 590
JO - Physica A: Statistical Mechanics and its Applications
JF - Physica A: Statistical Mechanics and its Applications
SN - 0378-4371
M1 - 126724
ER -
ID: 371847537